YES(?, a + 1) Initial complexity problem: 1: T: (?, 1) zip3(a, b, c) -> zip3(a - 1, b - 1, c - 1) [ a >= 1 /\ b >= 1 /\ c >= 1 ] (?, 1) group3(a, b, c) -> group3(a - 3, b, c) [ a >= 4 ] (1, 1) start(a, b, c) -> zip3(a, b, c) start location: start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: group3(a, b, c) -> group3(a - 3, b, c) [ a >= 4 ] We thus obtain the following problem: 2: T: (?, 1) zip3(a, b, c) -> zip3(a - 1, b - 1, c - 1) [ a >= 1 /\ b >= 1 /\ c >= 1 ] (1, 1) start(a, b, c) -> zip3(a, b, c) start location: start leaf cost: 0 A polynomial rank function with Pol(zip3) = V_1 Pol(start) = V_1 orients all transitions weakly and the transition zip3(a, b, c) -> zip3(a - 1, b - 1, c - 1) [ a >= 1 /\ b >= 1 /\ c >= 1 ] strictly and produces the following problem: 3: T: (a, 1) zip3(a, b, c) -> zip3(a - 1, b - 1, c - 1) [ a >= 1 /\ b >= 1 /\ c >= 1 ] (1, 1) start(a, b, c) -> zip3(a, b, c) start location: start leaf cost: 0 Complexity upper bound a + 1 Time: 0.155 sec (SMT: 0.149 sec)